+ & - Linear Expressions

Linear Expression - An algebraic expression in which the exponent of the variable is 1.
Examples: -4x 3X+5 5 - 1/6X

Like adding numbers, we can add linear expressions horizontally or vertically.

Horizontal Method

1. Change subtraction to addition using keep, change, change.
   
2. Eliminate parenthesis by using the distributive property.
   
3. Group like terms
   
4. Combine like terms ( don't forget to follow rules for adding integers!).
   

Example:

( -4y + 3 ) + ( 11y - 5 )

1. (-4y + 3) + (11y + -5)
   
2. -4y + 3 + 11y + -5
   
3. -4y + 11y + 3 + -5
   
4. 7y + -2 OR 7y - 2
   

Vertical Method

1. Align like terms vertically
   
2. Use keep, change, change within algebraic expressions to change subtraction to addition
   
3. Add ( don't forget the rules for adding integers!).
   

(x - 2 ) + ( 3x + 8 )

1. ( x - 2 )
   

+ ( 3x + 8)

2. ( x + -2)

+ ( 3x + 8)

3. 4x + 6

Like subtracting numbers, we can subtract linear expressions horizontally or vertically.

Horizontal method

1. Use keep change change within parenthesis to ensure that signs are correct
   
2. Use the distributive property to eliminate parenthesis
   
3. Group like terms
4. Combine like terms
   

Example
(7y + 5) - 2(4y - 3)

1. (7y + 5) - 2(4y + -3)
   
2. 7y + 5 - 8y + 6
   
3. 7y - 8y + 5 + 6
   
4. -y + 11

Vertical Method

1. Use keep change change to make sure that correct sign is used
   
2. Align terms vertically
   
3. Subtract
   

Example
(5x + 6) - (-x + 6)

1. ( 5x + 6) + (x + 6)
   
2. 5x + 6

+ x - 6
3. 6x